Set a large pot of water over high heat. While the water is heating up, use a sharp knife to score the bottom of each tomato with an X. Use a pairing knife to cut the core out of the top of each tomato. When the water is simmering, add the tomatoes and cook them for between 30 seconds and 1 minute. When the skin of the tomato looks like it is loosening or tearing slightly near the X that you cut, remove the tomatoes from the simmering water. Run cold water over the tomatoes to stop the cooking process. Keep the pot of water on the stove. You will use this same pot later to cook the pasta.
Cut the tomatoes into quarters and remove the skin from each tomato segment. Set a fine mesh strainer over a mixing bowl. Hold each tomato segment over the mesh strainer and remove the seeds. The bowl underneath the strainer will catch the "tomato water." The tomato water is delicious, and you will use it later in the recipe. The seeds can be discarded. You may need to cut a tomato segment in half in order to access and discard all the seeds. When all seeds have been removed, dice the tomato flesh into 1/4-inch pieces. When you are finished, you should have approximately 3 cups of chopped tomato flesh and 2/3 cup tomato water.
Set a large skillet over low heat and add the butter. When the butter has melted, add the garlic and adjust the heat to medium. Let the garlic sizzle and soften, stirring occasionally. When the garlic just begins to caramelize around the edges, add the diced tomato flesh. Season with salt and pepper, and cook until the tomato begins to break down and soften, stirring occasionally. Add the tomato water, and reduce the heat to low.
Bring the large pot of water back to a boil, add salt until the water tastes like the ocean, and cook your pasta according to the direction on the package, except undercook it by 1 to 2 minutes. Drain the pasta and add it to the skillet with the tomato sauce. If you feel like your skillet is too crowded, transfer everything to a large pot. Adjust the heat to high. Season lightly with salt and pepper.
Cook the pasta in the sauce, stirring regularly, until nearly all of the excess liquid in the sauce has evaporated. When nearly all excess liquid has evaporated, shut off the heat, and add the cheese. Stir vigorously as the cheese melts. Add the basil. Taste the pasta, and adjust with more salt and pepper as necessary. Serve and enjoy.
Born and raised in Brooklyn, I'm perpetually inspired by the diversity of foods that exist in this city. I love shopping at the farmer's market, making ingredients taste like the best versions of themselves, and rolling fresh pasta.